ua nt - p h / 03 10 15 6 v 1 2 6 O ct 2 00 3 Quantum and classical advantage distillation are not equivalent

We report that, for the generation of a secure cryptographic key from correlations established through a noisy quantum channel, the quantum and classical advantage distillation procedures are not equivalent, when coherent eavesdropping attacks are duly taken into account. The quantum procedure can tolerate markedly more noise in the channel than the classical procedure. One of the important problems in quantum cryptography is whether classical methods of key distillation are equivalent to quantum methods. This problem was recently investigated for a certain class of protocols in Refs. [1, 2, 3]. It was concluded there that the quantum entanglement distillation [4] tolerates exactly the same amount of errors in a raw cryptographic key as classical advantage distillation [5]. The analysis was carried out under the assumption that Eve performs the most general incoherent attack. In this short note [6] we report that this equivalence is only apparent, in fact classical advantage distillation is not as powerful as quantum entanglement distillation. This is so because Eve has the option of coherent attacks